On the Number of Paths of Lengths 3 and 4 in a Graph
In this paper, we obtain explicit formulae for the total number of paths of lengths 3 and 4 in a simple graph G. We also determine some formulae for the number of paths of lengths 3 and 4 each of which starts from an specific vertex vi and for the number of vi-vj paths of lengths 3 and 4 in a simple graph G, in terms of the adjacency matrix and with the helps of combinatorics.
Keywords: Adjacency Matrix, Cycle, Graph Theory, Path, Subgraph, Walk .
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